Plant organs grow symplastically, i.e. in a continuous and coordinated way. Such growth is of a tensor nature, which is manifested in the property that at every point of the organ three mutually orthogonal principal growth directions (PDG) can be recognized. The PDGs are postulated to affect orientation of cell divisions. This paper shows for the first time the 2D simulation model for growth in which cells divide taking into account the PDGs. The model, conceptually based on the growth tensor (GT), is applied to the root apex of radish, having a quiescent centre (QC). It shows the simulation of how exemplary cell pattern of the real root apex develops in time. The results provide satisfactory description of the root growth. The computer-generated cell pattern is realistic and more or less steady indicating that PDGs are important for growth. Presumably cells detect PDGs and obey them in the course of cell divisions. Computer generated division walls, perpendicular to PDGs, form periclinal and anticlinal zigzags as regular as those observed in microscopic sections. Growth tensor defines a field of growth rates at the organ level. QC, fundamental in this field, determines the group of quiescent initial cells which is, in turn, surrounded by active functional initials, from which all tissues of the root apex originate. The present simulations have shown that stability of generated cell pattern depends on whether the group of the functional initials is permanent; if this is not the case, the cell wall pattern changes in accordance with PDGs.
The effect of mechanical stress on the root apical meristem (RAM) organization of Zea mays was investigated. In the experiment performed, root apices were grown through a narrowing of either circular (variant I) or elliptical (variant II) shape. This caused a mechanical impedance distributed circumferentially or from the opposite sides in variant I and II, respectively. The maximal force exerted by the growing root in response to the impedance reached the value of 0.15 N for variant I and 0.08 N for variant II. Significant morphological and anatomical changes were observed. The changes in morphology depended on the variant and concerned diminishing and/or deformation of the cross-section of the root apex, and buckling and swelling of the root. Anatomical changes, similar in both variants, concerned transformation of the meristem from closed to open, an increase in the number of the cell layers at the pole of the root proper, and atypical oblique divisions of the root cap cells. After leaving the narrowing, a return to both typical cellular organization and morphology of the apex was observed. The results are discussed in terms of three aspects: the morphological response, the RAM reorganization, and mechanical factors. Assuming that the orientation of division walls is affected by directional cues of a tensor nature, the changes mentioned may indicate that a pattern of such cues is modified when the root apex passes through the narrowing, but its primary mode is finally restored.
In this work, the formation of the virtual lateral root (VLR) is shown. The VLR is formed using the 2D simulation model of growth and cell divisions based on the concept of growth tensor, specified for radish. Growth is generated by the field of growth rates of an unsteady type (GT field). Principal directions of growth (PDGs) are assumed to define the orientation of cell divisions. Temporal sequences of the VLR formation are a result of an application of the GT field to the polygon meshwork representing cell pattern of already initiated primordium. The computer-generated lateral root (LR) develops realistically, and its cell pattern is vivid and similar to that observed in anatomical sections. The real and virtual LRs show similar cellular organization, both originate from a small group of cells situated in two-cell layers of the pericycle and both layers are engaged in the LR development. The LR formation seems to be controlled at the tensor level and individual cells presumably detect PDGs and obey them in the course of the cell divisions. PDGs are postulated to affect the cellular organization of the LR. Using the method of computer simulations, cellular aspects of the LR morphogenesis are discussed.
In the cell pattern of the developing lateral root the principal directions of growth can be recognized through occurrence of oblique cell divisions. In simulation the role of these directions in cell pattern formation was confirmed, only when cells divide with respect to the principal directions can realistic results be obtained.
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